The Meijer G function is traditionally defined by an inverse Mellin transform
Hence the traditional definition is related to our definition by
The new notation has some advantages over the old notation. First, the parameters
of the Meijer G function are separated out into four natural groups
,
,
, and
. Second, possibly more controversial, we place
instead of
inside the integrand. We deem this desirable because of the "multivalued" character
of
. Finally, the
subscripts and superscripts which are now redundant are omitted.
